Queensland dominated the first two days of the season opener at the WACA Ground in Perth before WA produced a stunning fightback on Saturday.
After Richardson (5-19) ran riot to bowl Queensland out for 68, WA were just 67 runs away from chasing down the 201-run victory target at stumps on day three.
Richardson demanded the attention of Test selectors as Queensland collapsed to 5-13.
The 30-year-old has battled countless injuries in a stop-start international career, playing four Tests since debuting in 2019.
But a recall may be on the cards if he is fit and firing during a busy 12-month period in which Australia will play at least 20 Tests, with chief selector George Bailey having previously admitted the nation's depth will be tested across all formats.
The WA speedster hasn't given up hope of donning his baggy green again after getting his body right.
"Obviously I've had a small taste of it (Test cricket) and desperately want to get back there," Richardson said.
"It's just nice to be out there playing cricket and bowling a lot of overs.
"I had 30-odd overs in India (for Australia A), and then to back it up with another 29 or 30 here, I think it puts me in good stead for the rest of the season."
The odds looked stacked against WA at 5-83 after losing Cameron Bancroft (9), Hilton Cartwright (0), Joel Curtis (4), Sam Whiteman (40) and Corey Rocchiccioli (6).
But allrounder Aaron Hardie (48 not out) and paceman Joel Paris (19 not out) combined for a 51-run partnership to give WA the edge at 5-134 when poor light stopped play.
Uncertainty remains over whether Sam Fanning can bat if called upon on Sunday, after the New Zealand-born opener hobbled off with an apparent hamstring injury.
Under Cricket Australia's injury substitution trial, teams can only replace an injured or ill player in a regular-season Shield match until stumps on day two.
He added to WA's casualty ward after illness ripped through their camp, leading to the substitution of debutant Tom Murray on day two and Jayden Goodwin's late omission before the toss.
Left-armer Paris (3-21) struck twice in the first over of Queensland's second innings to remove openers Hugh Weibgen and Angus Lovell as he combined with Richardson to seize momentum.
Earlier, Test hopeful Xavier Bartlett (5-48) cleaned up the tail to skittle WA for 175 in their first innings.
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